Slope reasoning on paper

This is the pencil-and-paper form of the no-three-in-line problem, placing $11$ counters on the $8 \times 8$ grid. Record each counter as a coordinate pair and test a new placement by slope, including vertical and horizontal lines.

Write slopes as reduced fractions: two segments lie on the same line only if their reduced slopes match and they pass through a common point. Symmetry saves work: a solution reflected or rotated is still a solution, so you can search a small part of the board and generate the rest.